Bring all to a boil in a large saucepan, over high heat. Reduce heat and simmer gently. Occasionally mash the fruit until peaches are very tender and liquid begins to reduce.
Using a fairly fine mesh strainer or a layer of cheesecloth over a bowl, pour all of the contents of the pot into it. Let all liquid pour off, don't press down too hard or it will get cloudy. Discard solids. Ladle into jars and follow same canning instructions the Ball website.
When using in tea, dilute to your taste with black tea. Use probably a 1:6 mixture with 1 part syrup and 6 parts tea to start.
You don't need to can this if you are going to use it immediately. Just keep jar in fridge.